Non-diophantine Arithmetics In Mathematics, Physics And Psychology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-diophantine Arithmetics In Mathematics, Physics And Psychology write by Mark Burgin. This book was released on 2020-11-04. Non-diophantine Arithmetics In Mathematics, Physics And Psychology available in PDF, EPUB and Kindle. For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.
Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective
Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective write by Mark Burgin. This book was released on 2022-04-22. Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective available in PDF, EPUB and Kindle. The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology
Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology write by Paul Benioff. This book was released on 2024-01-19. Local Mathematics For Local Physics: From Number Scaling To Guage Theory And Cosmology available in PDF, EPUB and Kindle. The language of the universe is mathematics, but how exactly do you know that all parts of the universe 'speak' the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the 'value field'. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author's work in the context of a shift in the scientific paradigm looming on the horizon.
Non-Newtonian Calculus
Non-Newtonian Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Newtonian Calculus write by Michael Grossman. This book was released on 1972. Non-Newtonian Calculus available in PDF, EPUB and Kindle. The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Nevanlinna Theory And Its Relation To Diophantine Approximation
Nevanlinna Theory And Its Relation To Diophantine Approximation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nevanlinna Theory And Its Relation To Diophantine Approximation write by Min Ru. This book was released on 2001-06-06. Nevanlinna Theory And Its Relation To Diophantine Approximation available in PDF, EPUB and Kindle. It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects.Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems.
